Comparing Two Numbers

Comparing Two Numbers

When comparing two numbers, x and y, there are three possibilities:

  • x = y
  • x < y (x is less than y. The less than symbol points to the left.)
  • x > y (x is greater than y. The greater than symbol points to the right.)

Examples

  • Comparing 3 and 5: 3 < 5
  • Comparing 100 and 28: 100 > 28

Comparing Decimals

  • Start at the left and compare digits in the same place value.
  • Adding zeros to the end of the shorter decimal can be helpful to make comparison easier without changing the number's value. For example, 0.05 = 0.050 = 0.0500

Examples with Decimals

  1. Comparing 0.025 and 0.25
    • In the tenths place, 0.025 has a 0, while 0.25 has a 2. Since 0 < 2, 0.025 < 0.25. Adding a zero to the end of 0.25 to make it 0.250 can make the comparison easier.
  2. Comparing 2.875 and 2.785
    • In the tenths place, 2.875 has an 8, while 2.785 has a 7. Since 8 > 7, 2.875 > 2.785.

Comparing Negative Numbers

  • On the number line, the further left a number is, the smaller it is.
  • The negative side of the number line goes backward, meaning the further you get in the negative direction, the smaller you are.
  • Example: Comparing -9 and -2: -9 < -2

Additional Examples

  1. Comparing 0.75 and 0.749
    • They differ in the hundredths place. Since 5 > 4, 0.75 > 0.749. Adding a zero to the end of 0.75 to make it 0.750 can make the comparison easier.
  2. Comparing 0.05 and 0.050
    • Adding a zero to the end of a decimal doesn't change its value, so 0.05 = 0.050.
  3. Comparing 3.14 and 3.141
    • Adding a zero to the end of 3.14 to make it 3.140 can make the comparison easier. Since 0 < 1, 3.14 < 3.141.

Importance in Statistics

Accurately comparing two decimals is a very important skill to have for statistics.